SOLUTION: solve the equation using the -b +/- square root of b squared-4(a)(c)divided by 2a 1. I know the formula I just cannot figure this out. x squared = 196 Also if you can hel

Question 117161: solve the equation using the -b +/- square root of b squared-4(a)(c)divided by 2a
1. I know the formula I just cannot figure this out.
x squared = 196
Also if you can help with another.
x squared -4x +2 = 0
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1

Start with the given equation

Move all of the terms to the left side

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve (note: since the polynomial does not have an "x" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like notice , , and )

Plug in a=1, b=0, and c=-196

Square 0 to get 0

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

#2

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-4, and c=2

Negate -4 to get 4

Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or

Notice when we graph , we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. I know the formula I just cannot figure this out.
x squared = 196
x^2-196 = 0
x = [0 +-sqrt(0 - 4*196)]/2
x = [+- 28]/2
x = +14 or x= -14
-----------------------------
Also if you can help with another.
x squared -4x +2 = 0
x = [4 +- sqrt(16-4*2)]/2
x = [4 +- sqrt(8)]/2
x = 2 + sqrt2 or x = 2 - sqrt2
=======================
Cheers,
Stan H.

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